I'm making noodle soup tonight, but I accidentally bought Shanghai Style noodles instead of Udon noodles. They looked really similar so I guess I just grabbed it.
Can I use them for soups? Are the noodles the same?
They are not the same thing. See how the "Shanghai noodles" are yellow? That comes from alkali salts added to the dough which gives those noodles a firmer texture.
You certainly can use them for soups, they're just a little different than udon.